Describe a strategy for evaluating exponential functions for negative inputs.Use the examples if they help with your thinking.

Evaluating exponential functions for negative inputs can be done using the following steps:

1. Understand the Exponential Function: An exponential function is a mathematical function of the form f(x) = a^x, where 'a' is a positive real number, not equal to 1, and 'x' is any real number.

2. Negative Inputs: When we talk about negative inputs, we are referring to the 'x' in the function f(x) = a^x. So, if we have a function like f(x) = 2^x, and we want to evaluate it for x = -3, we would plug -3 in for x, giving us 2^-3.

3. Reciprocal Rule: The key to evaluating exponential functions for negative inputs is understanding that a^-n = 1/a^n. This is known as the reciprocal rule. So, if we have 2^-3, we can rewrite this as 1/2^3.

4. Evaluate: Now, we simply evaluate the expression. In our example, 2^3 = 8, so 1/2^3 = 1/8.

5. Conclusion: Therefore, the value of the function f(x) = 2^x at x = -3 is 1/8.

Remember, this strategy works for any base 'a' and any negative exponent 'x'. The key is understanding the reciprocal rule and applying it correctly.